Error

Try it out

Derivation

1. Initial program 0.8

   \[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
2. Using strategy rm

3. Applied add-sqr-sqrt0.8

   \[\leadsto \frac{\tan^{-1}_* \frac{im}{re}}{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}\]

4. Applied *-un-lft-identity0.8

   \[\leadsto \frac{\color{blue}{1 \cdot \tan^{-1}_* \frac{im}{re}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

5. Applied times-frac0.8

   \[\leadsto \color{blue}{\frac{1}{\sqrt{\log 10}} \cdot \frac{\tan^{-1}_* \frac{im}{re}}{\sqrt{\log 10}}}\]
6. Using strategy rm

7. Applied add-cube-cbrt0.8

   \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{1}{\sqrt{\log 10}}} \cdot \sqrt[3]{\frac{1}{\sqrt{\log 10}}}\right) \cdot \sqrt[3]{\frac{1}{\sqrt{\log 10}}}\right)} \cdot \frac{\tan^{-1}_* \frac{im}{re}}{\sqrt{\log 10}}\]

8. Applied associate-*l*0.9

   \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{\sqrt{\log 10}}} \cdot \sqrt[3]{\frac{1}{\sqrt{\log 10}}}\right) \cdot \left(\sqrt[3]{\frac{1}{\sqrt{\log 10}}} \cdot \frac{\tan^{-1}_* \frac{im}{re}}{\sqrt{\log 10}}\right)}\]
9. Using strategy rm

10. Applied cbrt-div0.8

    \[\leadsto \left(\sqrt[3]{\frac{1}{\sqrt{\log 10}}} \cdot \sqrt[3]{\frac{1}{\sqrt{\log 10}}}\right) \cdot \left(\color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{\sqrt{\log 10}}}} \cdot \frac{\tan^{-1}_* \frac{im}{re}}{\sqrt{\log 10}}\right)\]

11. Applied frac-times0.8

    \[\leadsto \left(\sqrt[3]{\frac{1}{\sqrt{\log 10}}} \cdot \sqrt[3]{\frac{1}{\sqrt{\log 10}}}\right) \cdot \color{blue}{\frac{\sqrt[3]{1} \cdot \tan^{-1}_* \frac{im}{re}}{\sqrt[3]{\sqrt{\log 10}} \cdot \sqrt{\log 10}}}\]

Runtime

Time bar (total: 3.4m)Debug logProfile

herbie shell --seed 2019053 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))